Question

What should be subtracted to the polynomial x ^2 - 5 x + 4, so that x - 3 is a factor of the resulting polynomial ?

options

2
-2
5
4​

Answer 1

Step-by-step explanation:

Given polynomial

$\red{ \pmb{x^2 - 5x + 4}}$

$\bf \: Let \: f(x) = x ^ 2 - 5x + 4 \\ \bf \: Subetbuting \: x = 3$

$\sf \: f(n) = 3 ^ 2 - 5(3) + 4 \\ \sf =9-15+4 \\ \sf = 13 - 15 \\ \sf =-2$

$\red{ \bf \therefore \: - 2 \: must \: be \: added \: }\\ \red{ \bf to \: f(X) \: such \: that }\\ \red{ \bf (x-3) \: is \: a \: factor  \: of  \: f(x) .}$

Hope it helps you✌️